Evaluate log base 25 of 125

Problem

(log_25)(125)

Solution

1. Identify the base and the argument of the logarithm. The base is 25 and the argument is 125

2. Express both numbers as powers of a common base. Since 25=5 and 125=5 we can rewrite the expression using base 5

3. Apply the change of base formula, which states (log_b)(a)=(log_c)(a)/(log_c)(b)

4. Substitute the values into the formula using c=5

(log_25)(125)=(log_5)(125)/(log_5)(25)

5. Evaluate the numerator and the denominator. Since 5=125 (log_5)(125)=3 Since 5=25 (log_5)(25)=2

6. Simplify the resulting fraction.

3/2=1.5

Final Answer

(log_25)(125)=3/2

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